The porous medium equation as a finite-speed approximation to a Hamilton-Jacobi equation
Annales de l'I.H.P. Analyse non linéaire (1987)
- Volume: 4, Issue: 3, page 203-230
- ISSN: 0294-1449
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topAronson, D. G., and Vazquez, J. L.. "The porous medium equation as a finite-speed approximation to a Hamilton-Jacobi equation." Annales de l'I.H.P. Analyse non linéaire 4.3 (1987): 203-230. <http://eudml.org/doc/78129>.
@article{Aronson1987,
author = {Aronson, D. G., Vazquez, J. L.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {porous medium flow; Hamilton-Jacobi equation; viscosity solutions interfaces; finite speed; propagation of disturbances},
language = {eng},
number = {3},
pages = {203-230},
publisher = {Gauthier-Villars},
title = {The porous medium equation as a finite-speed approximation to a Hamilton-Jacobi equation},
url = {http://eudml.org/doc/78129},
volume = {4},
year = {1987},
}
TY - JOUR
AU - Aronson, D. G.
AU - Vazquez, J. L.
TI - The porous medium equation as a finite-speed approximation to a Hamilton-Jacobi equation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1987
PB - Gauthier-Villars
VL - 4
IS - 3
SP - 203
EP - 230
LA - eng
KW - porous medium flow; Hamilton-Jacobi equation; viscosity solutions interfaces; finite speed; propagation of disturbances
UR - http://eudml.org/doc/78129
ER -
References
top- [A1] D.G. Aronson, Regularity properties of flows through porous media, SIAM J. Appl. Math., t. 17, 1969, p. 461-467. Zbl0187.03401MR247303
- [A 2] D.G. Aronson, Regularity properties of flows through porous media: the interface, Arch. Rational Mech. Anal., t. 37, 1970, p. 1-10. Zbl0202.37901MR255996
- [AB] D.G. Aronson, Ph. Bénilan, Régularité des solutions de l'équation des milieux poreux dans R", C. R. Acad. Sci. Paris, t. 288, 1979, p. 103-105. Zbl0397.35034MR524760
- [AC] D.G. Aronson, L.A. Caffarelli, The initial trace of a solution of the porous medium equation, Trans. Amer. Math. Soc., t. 280, 1983, p. 351-366. Zbl0556.76084MR712265
- [ACK] D.G. Aronson, L.A. Caffarelli, S. Kamin, How an initially stationary interface begins to move in porous medium flow, SIAM J. Math. Anal., t. 14, 1983, p. 639-658. Zbl0542.76119MR704481
- [ACV] D.G. Aronson, L.A. Caffarelli, J.L. Vazquez, Interfaces with a corner-point in one-dimensional porous medium flow, Comm. Pure Applied Math., t. 38, 1985, p. 375-404. Zbl0544.35058MR792397
- [BC 1] Ph. Bénilan, M.G. Crandall, The continuous dependence on φ of the solutions of ut - Δφ(u) = 0, Indiana Univ. Math. J., t. 30, 1981, p. 161-177. Zbl0482.35012MR604277
- [BC2] Ph. Bénilan, M.G. Crandall, Regularizing effects of homogeneous evolution equations, Contributions to Analysis and Geometry, Supplement to American J. Math., D. N. Clark et al. eds., Baltimore, 1981, p. 23-39. Zbl0556.35067MR648452
- [BCP] Ph. Bénilan, M.G. Crandall, M. Pierre, Solutions of the porous medium equation in R'' under optimal conditions on initial values, Indiana Univ. Math. J., t. 33, 1984, p. 51-87. Zbl0552.35045MR726106
- [BV] Ph. Bénilan, J.L. Vazquez, Concavity of solutions of the porous medium equation, to appear in Trans. Amer. Math. Soc. Zbl0628.76092MR869400
- [B] S.H. Benton, The Hamilton-Jacobi equation : a global approach, Academic Press, New York, 1977. Zbl0418.49001MR442431
- [CF] L.A. Caffarelli, A. Friedman, Regularity of the free-boundary for the one-dimensional flow of gas in a porous medium, Amer. J. Math., t. 101, 1979, p. 1193-1218. Zbl0439.76084MR548877
- [CEL] M.G. Crandall, L.C. Evans, P.L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., t. 282, 1984, p. 487-502. Zbl0543.35011MR732102
- [CL] M.G. Crandall, P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., t. 277, 1983, p. 1-42. Zbl0599.35024MR690039
- [D] C.M. Dafermos, Characteristics in hyperbolic conservation laws in Nonlinear Analysis and Mechanics, Vol. I, ed. R. J. Knops, London, Pitman, 1977, p. 1-58. Zbl0373.35048MR481581
- [DK] B.E. Dahlberg, C.E. Kenig, Nonnegative solutions of the porous medium equation, Comm. Partial Diff. Equations, t. 9, 1984, p. 409-437. Zbl0547.35057MR741215
- [G] B.H. Gilding, Hölder continuity of solutions of parabolic equations, J. London Math. Soc., t. 13, 1976, p. 103-106. Zbl0319.35045MR399658
- [GJ] J.L. Graveleau, P. Jamet, A finite-different approach to some degenerate non-linear parabolic equations, SIAM J. Appl. Math., t. 20, 1971, p. 199-223. Zbl0226.65065MR290600
- [HP] M.A. Herrero, M. Pierre, The Cauchy problem for ut = Δum when 0 < m < 1, Trans. Amer. Math. Soc., t. 290, 1985, p. 1-14.
- [H] E. Hopf, The partial differential equation ut + uux = μuxx. Comm. Pure Applied Math., t. 3, 1950, p. 201-230. Zbl0039.10403MR47234
- [K] S. Kamin, The asymptotic behaviour of the solution of the filtration equation, Israel J. Math., t. 14, 1973, p. 76-78. Zbl0254.35054MR315292
- [KC] W.L. Kath, D.S. Cohen, Waiting time behaviour in a nonlinear diffusion equation. Studies in Applied Maths., t. 67, 1982, p. 79-105. Zbl0499.76078MR670736
- [Kn] B. Knerr, The porous medium equation in one dimension, Trans. Amer. Math. Soc., t. 234, 1977, p. 381-415. Zbl0365.35030MR492856
- [La] P.D. Lax, Hyperbolic systems of conservation laws II, Comm. Pure Applied Math., t. 10, 1957, p. 537-566. Zbl0081.08803MR93653
- [Li] P.L. Lions, Generalized solutions of Hamilton-Jacobi equations, Research Notes in Math. # 69, Pitman, Boston, 1982. Zbl0497.35001MR667669
- [LSV] P.L. Lions, P.E. Souganidis, J.L. Vazquez, In preparation.
- [LP] T.-P. Liu, M. Pierre, Source-solutions and asymptotic behavior in conservation laws, J. Diff. Equations, t. 51, 1984, p. 419-441. Zbl0545.35057MR735207
- [O] O.A. Oleinik, Discontinuous solutions of nonlinear differential equations, Amer. Math. Soc. Translations, t. 26, (2), 1983, p. 95-172. Doklady Akad. Nauk SSSR, t. 109, 1956, p. 1098-1101 (in Russian). Zbl0131.31803MR83088
- [OKC] O.A. Oleinik, A.S. Kalashnikov, Y.L. Czhou, The Cauchy problem and boundary problems for equations of the type of nonstationary filtration, lzv. Akad. Nauk SSSR Ser. Mat., t. 22, 1958, p. 667-704 (in Russian). MR99834
- [V1] J.L. Vazquez, Asymptotic behaviour and propagation properties of the one-dimensional flow of a gas in a porous medium, Trans. Amer. Math. Soc., t. 277, 1983, p. 505-527. Zbl0528.76096MR694373
- [V2] J.L. Vazquez, Behaviour of the velocity of one-dimensional flows in porous media, Trans. Amer. Math. Soc., t. 286, 1984, p. 787-802. Zbl0524.35014MR760987
- [V3] J.L. Vazquez, The interfaces of one-dimensional flows in porous media, Trans. Amer. Math. Soc., t. 285, 1984, p. 717-737. Zbl0524.35060MR752500
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